Voozh

A380288

a(n) is the number of divisors d of n such that 2^d - 1 is not prime.

1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 2, 4, 1, 2, 2, 4, 1, 4, 1, 4, 2, 3, 2, 6, 2, 2, 3, 4, 2, 5, 1, 5, 3, 2, 2, 7, 2, 2, 2, 6, 2, 5, 2, 5, 4, 3, 2, 8, 2, 4, 2, 4, 2, 6, 3, 6, 2, 3, 2, 9, 1, 2, 4, 6, 2, 6, 2, 4, 3, 5, 2, 10, 2, 3, 4, 4, 3, 5, 2, 8, 4, 3, 2, 9, 2, 3, 3, 7, 1, 9, 2, 5, 2, 3, 2, 10, 2, 4, 5, 7

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Table of n, a(n) for n=1..100.

FORMULA

a(n) = A000005(n) - A379590(n).

MATHEMATICA

a[n_] := DivisorSum[n, 1 &, !PrimeQ[2^# - 1] &]; Array[a, 100] (* Amiram Eldar, Jan 19 2025 *)

PROG

(Magma) [#[d: d in Divisors(n) | not IsPrime(2^d-1)]: n in [1..100]];

(PARI) a(n) = sumdiv(n, d, !isprime(2^d - 1)); \\ Michel Marcus, Jan 19 2025